The role of definition in students' understanding with particular reference to the concavity of a function

Abstract

In this study, the effect of different definitions of concavity on students' understanding was investigated. Students enrolled in the calculus-II course in the science and engineering faculties in Anadolu University, Turkey were divided into two groups and each group was given a different definition of concavity. At the end of the study, both groups' understanding was observed to depend on the definition. Another observation is that both groups can apply the second derivative test as well as each other.